I think the issue is that you can fire someone for no reason but you can't fire them for a wrong reason, even if a "right to work" state.

I haven't seen this in law but I worked for a very large company in a "right to work" state and this is how they behaved in all things. If you were fired you would never be told why. If you called for a reference you would be told the length of employment and last position held. Nothing more. I don't think they went to all that trouble for no reason.